Question: The equation of a circle $C$ is $x^2+y^2+12x-12y+63 = 0$. What is its center $(h, k)$ and its radius $r$ ?
Solution: To find the equation in standard form, complete the square. $(x^2+12x) + (y^2-12y) = -63$ $(x^2+12x+36) + (y^2-12y+36) = -63 + 36 + 36$ $(x+6)^{2} + (y-6)^{2} = 9 = 3^2$ Thus, $(h, k) = (-6, 6)$ and $r = 3$.